The Virtues and Vices of Simplicity

by johnmccreery

I know, I’m rushing the fences a bit. But I’m just at the point in Miller and Page when, having whetted our appetites with simple examples, they are getting ready to ratchet up the complexity. They pause to review a few key points. Two paragraphs leap out at me.

While our model gives us some useful intuitions and insights, it is also (quite intentionally) very limited. Like all good models, it was designed to be just sufficient to tell a story that could be understood easily yet have enough substance to provide some insights into broader issues.

This view of the role of models as “just sufficient to tell a story” yet “have enough substance to provide some insights” strikes me as very important. It wards off the nay-sayers who want the whole truth — making any story but one told by an omniscient God insufficient. Yet it also demands more than a casual tale based on mere opinion. It allows the serious critic to demand some beef without insisting on the whole cow.

What, then, of formal elegance and the difference between simple formulas and the computational use of formulaic rules to which Asher directs our attention?

In economics, formal modeling usually proceeds by developing mathematical models derived from first principles. This approach, when well practiced, results in very clean and stark models that yield key insights. Unfortunately, while such a framework imposes a useful discipline on the modeling, it also can be quite limiting. The formal mathematical approach works best for static, homogeneous, equilibrating worlds. Even in our very simple example [the towns with the two kinds of chillies], we are beginning to violate these desiderata. Thus, if we want to investigate richer, more dynamic worlds, we need to pursue other modeling approaches. The trade-off, of course, is that we must weigh the potential to generate new insights against the cost of having less exacting analytics.

My eye is drawn to the word “trade-off,” a term with which practical politicians, business people, and engineers are comfortable but, if Deirdre McCloskey is right in “Bourgeois Virtue,” most academics are not. Academics, McCloskey suggests, tend to favor either aristocratic or peasant views of virtue; one asserts a punctilious view of honor, the other fiercely defends a turf; both cling to positions and regard the compromises that “trade-off” implies with disdain. It’s the difference between, “Is that assumption right or wrong?” and the more pragmatic “What does that assumption buy us?”

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13 Comments to “The Virtues and Vices of Simplicity”

  1. On some level (one that I thought important), my dissertation was an exercise in using Wittgenstein to develop a different way of thinking about “models,” or, more accurately, about how to ask and answer questions in a social-scientific-ish way. My efforts were spurred in part by the fact that my department had (a) a bunch of Straussians and (b) a bunch of game theorists. I found the game theorists, in particular, to be a pain, because I found their models drained life of its interesting bits without providing sufficient insight in return. (The Straussians were off in their own world, and, really, Wittgenstein was the counter to them as well.)

    So, then, the question becomes when a “simple” model really IS useful, and my answer, at least in grad school, was “not nearly as often as you seem to think it is.”

  2. Narya, how wonderfully academic you sound . But, seriously, when I was in graduate school, now four decades ago, I asked similar questions and came to a similar place in my own thinking — that is how I wound up excited about Victor Turner and writing a dissertation on the symbolism of Daoist magic. The simple models of that era all seemed too simplistic.

    As I just said, however, that was four decades ago, and a lot has happened since then. If you were to ask me if any of the simple models I have described so far is an adequate description of social reality, I would reply, “Of course not.” If, on the other hand, you were to ask if they looked like interesting starting points for developing ideas about social reality, taking advantage of advances in computing and simulation software, I would reply, “Maybe.”

    So far the book looks good, pleasantly modest in tone and nicely paced for a reader like me, who knows a bit about the relevant math and other technology involved. The notion that I might stop because someone invokes the sacred name of a white male who was dead before I started graduate school? No, that doesn’t make sense to me. Wittgenstein taught us a lot; but now we have a lot of new ways to play our language games, using techniques that require neither Tractatus-like efforts to formalize everything we can possibly know nor endless thick descriptions that never go anywhere. I’d like to give them a try and see where they take me.

  3. Oh, yes, the books you’re telling us about DO sound interesting! I was piling on in agreement, not disparaging!

    Wittgenstein of the Tractatus did nothing for me; I’m a Philosophical Investigations woman all the way. What I was trying to do is get beyond the “thick descriptions” school, as well, because, ultimately, you just end up with a lot of interesting stories. And, actually, I thought (and think) that language games as a metaphor is useful in the way that other models can be useful: if part of what one is doing is trying to find the rules in play in a particular arena, then you are, indeed, using some model-type questions.

  4. Narya – your dissertation sounds extremely interesting. For a while, I have had in the back of my head a fiction piece in which someone from the near-present goes back in time and tells Wittgenstein (late Wittgenstein) about neural networks. It has always struck me that the Wittgenstein of Philosophical Investigations was right on the edge of an even richer way of looking at things, and that neural networks (really, agent-based simulations) would have given him the metaphor he needed.

  5. John – I like what you say about trade-offs. It also plays into the concept of “reduction” that I so often go on about. One could say that the universe is a non-reductive simulation of itself.

  6. Adequate for what? The map is not the territory, and a good thing, too. Borges:

    On Exactitude in Science . . . In that Empire, the Art of Cartography attained such Perfection that the map of a single Province occupied the entirety of a City, and the map of the Empire, the entirety of a Province. In time, those Unconscionable Maps no longer satisfied, and the Cartographers Guilds struck a Map of the Empire whose size was that of the Empire, and which coincided point for point with it. The following Generations, who were not so fond of the Study of Cartography as their Forebears had been, saw that that vast Map was Useless, and not without some Pitilessness was it, that they delivered it up to the Inclemencies of Sun and Winters. In the Deserts of the West, still today, there are Tattered Ruins of that Map, inhabited by Animals and Beggars; in all the Land there is no other Relic of the Disciplines of Geography.

  7. Thanks, Asher; I had fun writing it, actually. I was trying to do multiple things with it. For one, I was trying to get out of the Popper vs. the nihilists box, and I saw Wittgenstein as a useful way to do that. For a second, I was trying to see if one could, in fact, “use Wittgenstein” as the basis for a social science methodology, one that avoided the Weberian desire for and claims of Scientific Objectivity but that also enabled us to take positions. And, for a third, I did some actual investigations (I examined two “divisions of labor” that we generally take for granted in our speech, and I looked at each of them in a slightly different way; in particular, I examined how public school teachers, administrators, boards of education, etc., talked about whether teachers were workers or professionals–which became a huge point of contention as teachers organized, and I looked at how several popular American magazines talked about men’s work and women’s work. Thus, the former was a kind of ground-up question–how did real people fight about this–and the second was kind of top-down–what were the more general messages being transmitted by means of what at one time was a major mass medium. Did I mention that I had a LOT of fun?

  8. p.s. the epigraph at the very beginning was “The map is not the territory.”

  9. @Narya

    Your dissertation does sound fascinating. Could you tell us a bit more about it? How did Wittgenstein help you with the analyses you conducted? Inspiration? Metaphor? Technique?

    @Asher

    What do you envision Wittgenstein making of neural networks? Again, just looking for a bit more detail.

  10. I don’t remember any more exactly what my path was. I hadn’t read LW before I took a class in grad school, and he immediately grabbed my attention (again, the Investigations, not the Tractatus). When I was in school, there were (and, for all I know, still are) lots of divisions between the people who wanted to cling to an Objective Truth in a kind of Weberian/Popperish way and people who wanted to claim that everything was all only thick description (obviously I”m exaggerating somewhat). In particular, the former seemed to regard language as a clear pane of glass through which one viewed the world, while the latter regarded it as, I don’t know, ALL language.

    What I liked about LW is that he saw language and practice as importantly (rather than trivially) intertwined. I also liked his notion of boundaries for a purpose, as well as, of course, language games. So, I thought, how could one actually USE LW to conduct a social science investigation? Toward what kinds of things would his work point one’s attention? Which is what made me think about divisions of labor–in particular, two that we take for granted in our language and, in some ways, in our practice. In the case of the teachers, I was able to find people fighting over exactly that division–teachers shouldn’t organize because they are professionals! If teachers were professionals, then they would be better paid and, possibly more important, would have control over their work! Thus, looking at the argument enabled me to show that the whole thing is socially constructed–but with a much thicker/deeper notion of that, i.e., I didn’t use “socially constructed” as shorthand for “random.” It also enabled me to see where the pressure points were, particularly the points where particular kinds of power came into play.

    the other part, the part with the magazines, enabled me to look at a “higher-level” message. I couldn’t point to a particular article and argue that it caused a particular person to act in a particular way (and didn’t aim to do that), but if a whole lot of articles are fussing about a subject in a particular way, it is likely an arena of tension and disagreement.

    I would say that the other influence, though I didn’t discuss him much in my dissertation (if at all? don’t remember) was Bourdieu, to whom Carl’s dad had introduced me. (And whom I got to meet while in grad school; he was quite amusing.)

  11. John – I provide a little more detail in the comments to an old post by Kvond, if you want to take a look. The discussion didn’t end up being too illuminating, but my first comment points to what I was thinking. Another place in PI where I was thinking these thoughts is where LW discusses “families” of games, and the fact that there is no one quality shared by all games. This sort of mysterious categorization is made much less mysterious when one understands how neural networks categorize stuff (cognitively, you end up with radial categories, like Langacker talked about).

  12. Asher, the no-one-shared-quality and notion of families of games were something I think I used, too.

  13. @Asher, @Narya

    If you don’t know it already, you both might enjoy a look at George Lakoff’s Women, Fire and Dangerous Things, in which the cognitive scientist/linguist brings together a bunch of ideas with their own family resemblances. Here you can see Wittgenstein discussed alongside prototype theory, base terms, fuzzy logic, and a bunch of other attempts to get at how humans actually think and use language.

    My question for you both is, I can where what you have written makes effective use of family resemblance as a metaphor. Could it be pushed further, formalized in a way that would support convincing stimulations, if not explanations?

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